360,180,120,90, x , y 

 equals to 
 equals to 
 equals to 
So inductively,
 must equal to 
 
5x = 360
 x = 72
Also inductively,
 or  must equal to 
      
     6y = 360
      y = 60

360,180,120,90, 72 , 60 .

-------------------------------------

 1,5,14,30,55, x , y 

  5-1 equals to 4, which equals to 2².
 14-5 equals to 9, which equals to 3².
30-14 equals to 16, which equals to 4².
55-30 equals to 25, which equals to 5².

So inductively,
x-55 must equal to 6² or 36
x-55 = 36
   x = 91
 
Also inductively,
y-x or y-91 must equal to 7² or 49
       y-91 = 49
          y = 140

 1,5,14,30,55, 91 , 140 .

Edwin